Characterization of continuously distributed cortical water diffusion rates with a stretched‐exponential model

TLDR

Diffusion‑weighted imaging shows signal attenuation consistent with a multicompartmental theory, but the source of nonexponential behavior is debated because cortical micro‑heterogeneity complicates modeling. The study aims to account for cortical heterogeneity by developing a stretched‑exponential model to describe diffusion‑related signal decay without assuming a fixed number of sources. The authors performed spin‑echo diffusion‑weighted imaging on six rats with b‑values 500–6500 s/mm² and employed a stretched‑exponential function, introducing a distributed diffusion coefficient to quantify mean intravoxel rates. Fitting the data revealed that 20 % of voxels were better described by the stretched‑exponential model than by a biexponential one, indicating substantial intravoxel heterogeneity in the cerebral cortex. Magn Reson Med 50:727–734, 2003; © 2003 Wiley‑Liss, Inc.

Abstract

Abstract Experience with diffusion‐weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so‐called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched‐exponential function was developed to describe diffusion‐related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin‐echo diffusion‐weighted pulse sequence with b ‐values of 500–6500 s/mm 2 in six rats. Signal attenuation curves were fit to a stretched‐exponential function, and 20% of the voxels were better fit to the stretched‐exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Magn Reson Med 50:727–734, 2003. © 2003 Wiley‐Liss, Inc.